Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One
S. N. LakaevDepartment of Mathematics, Samarkand State University, University Boulevard 15, Samarkand 140104, UzbekistanArsmah IbrahimDepartment of Mathematics, Faculty of Computer science and Mathematics, MARA University Technology, 40450 Shah Alam, Selangor Darul Ehsan, MalaysiaShaxzod KurbanovDepartment of Mathematics, Samarkand State University, University Boulevard 15, Samarkand 140104, Uzbekistan
ABI
Аннотация
A family H μ ( p ), μ > 0, p ∈ 𝕋 2 of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two‐dimensional lattice ℤ 2 is considered. The existence or absence of the unique eigenvalue of the operator H μ ( p ) lying below threshold depending on the values of μ > 0 and p ∈ U δ (0) ⊂ 𝕋 2 is proved. The analyticity of corresponding eigenfunction is shown.
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